orders and structure of classical groups
Theorem 1.
$$\begin{array}{cc}\hfill SL(d,q)={q}^{\left(\genfrac{}{}{0pt}{}{d}{2}\right)}\prod _{i=2}^{d}({q}^{i}1),\hfill & \hfill PSL(d,q)=\frac{SL(d,q)}{(d,q1)},\hfill \\ \hfill GL(d,q)={q}^{\left(\genfrac{}{}{0pt}{}{d}{2}\right)}\prod _{i=1}^{d}({q}^{i}1),\hfill & \hfill PGL(d,q)=\frac{GL(d,q)}{q1},\hfill \\ \hfill \mathrm{\Gamma}L(d,q)=(q1){q}^{\left(\genfrac{}{}{0pt}{}{d}{2}\right)}\prod _{i=1}^{d}({q}^{i}1),\hfill & \hfill P\mathrm{\Gamma}L(d,q)=\frac{\mathrm{\Gamma}L(d,q)}{q1}.\hfill \end{array}$$ 
A proof of this theorem can proceed in many directions which each explain more of the structure of the these groups so each approach is considered equally valid and presented here. We list them from most elementary to most theoretical.

1.
Elementary linear algebra^{} proof (http://planetmath.org/ElementaryProofOfOrders)

2.
Proof from subgroups of $GL(V)$ (http://planetmath.org/TheoryFromOrdersOfClassicalGroups2)

3.
Proof from Lie theory/Chevally groups. [PENDING.]
Title  orders and structure of classical groups 

Canonical name  OrdersAndStructureOfClassicalGroups 
Date of creation  20130322 15:56:45 
Last modified on  20130322 15:56:45 
Owner  Algeboy (12884) 
Last modified by  Algeboy (12884) 
Numerical id  10 
Author  Algeboy (12884) 
Entry type  Topic 
Classification  msc 11E57 
Classification  msc 05E15 